On a variational problem arising in crystallography

Alexander J. Zaslavski

ESAIM: Control, Optimisation and Calculus of Variations (2007)

  • Volume: 13, Issue: 1, page 72-92
  • ISSN: 1292-8119

Abstract

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We study a variational problem which was introduced by Hannon, Marcus and Mizel [ESAIM: COCV9 (2003) 145–149] to describe step-terraces on surfaces of so-called “unorthodox” crystals. We show that there is no nondegenerate intervals on which the absolute value of a minimizer is π / 2 identically.

How to cite

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Zaslavski, Alexander J.. "On a variational problem arising in crystallography ." ESAIM: Control, Optimisation and Calculus of Variations 13.1 (2007): 72-92. <http://eudml.org/doc/249925>.

@article{Zaslavski2007,
abstract = { We study a variational problem which was introduced by Hannon, Marcus and Mizel [ESAIM: COCV9 (2003) 145–149] to describe step-terraces on surfaces of so-called “unorthodox” crystals. We show that there is no nondegenerate intervals on which the absolute value of a minimizer is $\pi/2$ identically. },
author = {Zaslavski, Alexander J.},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Minimizer; surfaces of crystals; unorthodox crystal; variational problem.; variational problem.},
language = {eng},
month = {2},
number = {1},
pages = {72-92},
publisher = {EDP Sciences},
title = {On a variational problem arising in crystallography },
url = {http://eudml.org/doc/249925},
volume = {13},
year = {2007},
}

TY - JOUR
AU - Zaslavski, Alexander J.
TI - On a variational problem arising in crystallography
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2007/2//
PB - EDP Sciences
VL - 13
IS - 1
SP - 72
EP - 92
AB - We study a variational problem which was introduced by Hannon, Marcus and Mizel [ESAIM: COCV9 (2003) 145–149] to describe step-terraces on surfaces of so-called “unorthodox” crystals. We show that there is no nondegenerate intervals on which the absolute value of a minimizer is $\pi/2$ identically.
LA - eng
KW - Minimizer; surfaces of crystals; unorthodox crystal; variational problem.; variational problem.
UR - http://eudml.org/doc/249925
ER -

References

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  1. B. Dacorogna and C.E. Pfister, Wulff theorem and best constant in Sobolev inequality. J. Math. Pures Appl.71 (1992) 97–118.  Zbl0676.46031
  2. I. Fonseca, The Wulff theorem revisited. Proc. R. Soc. Lond. A432 (1991) 125–145.  Zbl0725.49017
  3. J. Hannon, N.C. Bartelt, B.S. Swartzentruber, J.C. Hamilton and G.L. Kellogg, Step faceting at the (001) surface of boron doped silicon. Phys. Rev. Lett.79 (1997) 4226–4229.  
  4. J. Hannon, M. Marcus and V.J. Mizel, A variational problem modelling behavior of unorthodox silicon crystals. ESAIM: COCV9 (2003) 145–149.  Zbl1066.49011
  5. H.C. Jeng and E.D. Williams, Steps on surfaces: experiment and theory. Surface Science Reports34 (1999) 175–294.  
  6. W.W. Mullins, Theory of thermal grooving. J. Appl. Physics28 (1957) 333–339.  

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